Random bright pixels are being rendered
Those are refered to as fireflies - search for "reducing fireflies" for ideas of how to reduce/remove them. They look like the result of Caustics - the light reflected or refracted from (usually curved) surfaces. You can disable Caustics in the Render settings Light Paths panel - disable Reflective Caustics and Refractive Caustics and see if that helps. Alternatively, significantly increase your number of samples - but bear in mind you need a lot of samples to render good quality caustics.